Froggatt-Nielsen models with a residualZ4Rsymmetry

Abstract

The Froggatt-Nielsen mechanism provides an elegant explanation for the hierarchies of fermion masses and mixings in terms of a $U(1)$ symmetry. Promoting such a family symmetry to an $R$ symmetry, we explicitly construct supersymmetric Froggatt-Nielsen models which are gauged, family-dependent $U(1{)}_{R}$ completions of the ${\mathbb{Z}}_{4}^{R}$ symmetry proposed by Lee, Raby, Ratz, Ross, Schieren, Schmidt-Hoberg and Vaudrevange in 2010. Forbidden by ${\mathbb{Z}}_{4}^{R}$, the $\ensuremath{\mu}$ term is generated around the supersymmetry breaking scale ${m}_{3/2}$ from either the K\"ahler potential or the superpotential. Neutrinos acquire their mass via the type-I seesaw mechanism with three right-handed neutrino superfields. Taking into account the Green-Schwarz anomaly cancellation conditions, we arrive at a total of $3\ifmmode\times\else\texttimes\fi{}34$ distinct phenomenologically viable charge assignments for the standard model fields, most of which feature highly fractional charges.